Giải phương trình: \(\dfrac{10x}{\sqrt{10x+1}-1}=\sqrt{10x+20}\)
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ĐKXĐ : \(x\ge-\dfrac{3}{8}\)
Ta có : \(\sqrt{8x+3}=9x^2+10x+\dfrac{9}{4}\)
\(\Leftrightarrow36x^2+40x+9-4\sqrt{8x+3}=0\)
\(\Leftrightarrow\left(36x^2+48x+16\right)-8x-3-4\sqrt{8x+3}-4=0\)
\(\Leftrightarrow\left(6x+4\right)^2-\left(\sqrt{8x+3}+2\right)^2=0\)
\(\Leftrightarrow\left(6x+\sqrt{8x+3}+6\right).\left(6x+2-\sqrt{8x+3}\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{8x+3}=-6x-6\left(1\right)\\\sqrt{8x+3}=-6x-2\left(2\right)\end{matrix}\right.\)
Giải (1) ta có :
(1) <=> \(8x+3=\left(-6x-6\right)^2\) (với \(-6x-6\ge0\Leftrightarrow x\le-1\))
\(\Leftrightarrow36x^2+64x+33=0\)
\(\Leftrightarrow\left(6x+\dfrac{16}{3}\right)^2+\dfrac{41}{9}=0\)
\(\Leftrightarrow x\in\varnothing\) => (1) vô nghiệm
Giải (2) ta có
(2) <=> \(8x+3=\left(-6x-2\right)^2\) (với \(x\le-\dfrac{1}{3}\)) (*)
\(\Leftrightarrow36x^2+16x+1=0\)
\(\Leftrightarrow x=\dfrac{-4\pm\sqrt{7}}{18}\)
Kết hợp (*) và ĐKXĐ ta được \(x=\dfrac{-4+\sqrt{7}}{18}\) là nghiệm phương trình
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`a,3x^2+7x+2=0`
`<=>3x^2+6x+x+2=0`
`<=>3x(x+2)+x+2=0`
`<=>(x+2)(3x+1)=0`
`<=>x=-2\or\x=-1/3`
d) Ta có: (x-1)(x+2)=70
\(\Leftrightarrow x^2+2x-x-2-70=0\)
\(\Leftrightarrow x^2+x-72=0\)
\(\Leftrightarrow x^2+9x-8x-72=0\)
\(\Leftrightarrow x\left(x+9\right)-8\left(x+9\right)=0\)
\(\Leftrightarrow\left(x+9\right)\left(x-8\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+9=0\\x-8=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-9\\x=8\end{matrix}\right.\)
Vậy: S={8;-9}
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a) Ta có: \(\sqrt{x-2\sqrt{x-1}}-\sqrt{x-1}=1\)
\(\Leftrightarrow\left|\sqrt{x-1}-1\right|=\sqrt{x-1}+1\)
\(\Leftrightarrow\sqrt{x-1}=\sqrt{x-1}+1+1\)(Vô lý)
Vậy: \(S=\varnothing\)
b) Ta có: \(\sqrt{x^4+2x^2+1}=\sqrt{x^2+10x+25}-10x+22\)
\(\Leftrightarrow x^2+1=\left|x+5\right|-10x+22\)
\(\Leftrightarrow\left|x+5\right|=x^2+1+10x-22=x^2+10x-21\)
\(\Leftrightarrow\left[{}\begin{matrix}x+5=x^2+10x-21\left(x\ge-5\right)\\-x-5=x^2+10x-21\left(x< -5\right)\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x^2+10x-21-x-5=0\\x^2+10x-21+x+5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x^2+9x-26=0\\x^2+11x-16=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{-9+\sqrt{185}}{2}\\x=\dfrac{-11-\sqrt{185}}{2}\end{matrix}\right.\)
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a)
\(=\sqrt{10\left(x+2\right)}=\sqrt{10}.\sqrt{x+2}\)
\(\sqrt{x+2}\ge0=>x+2\ge0=>x\ge-2\)
b)
\(=\dfrac{\sqrt{99}}{\sqrt{4x-1}}\)
\(=>4x-1>0=>4x>1=>x>\dfrac{1}{4}\)
c)
\(=\dfrac{\sqrt{-5x-10}}{\sqrt{2021}}=>-5x-10\ge0\)
\(=>-5\left(x+2\right)\ge0\)
\(=>x+2\ge0=>x\ge-2\)
a: ĐKXĐ: \(x\ge-2\)
b: ĐKXĐ: \(x>\dfrac{1}{4}\)
c: ĐKXĐ: \(x\le-2\)
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